Update:
pvanroos fixed the issue :
"I fixed it by revoking access and then reauthorizing. The new org and role was added after I initially authorized access so that's why only my personal org was showing."
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@pvanroos , Based on my understanding of your issue description, you are referring to this specific option? ( screenshot below).
One possible reason for this is that you have not granted Azure access to the organization where the repository is located. Kindly ensure or double-check, that you need to authorize Azure to access your GitHub account and grant it access to the organization.
If you have already authorized Azure to access your GitHub account and the organization is still not showing up in the dropdown list, you may need to double-confirm your permissions in the organization ( I understand you have validate this already).
Also, please try to grant the access to the organization you want to see while creating the Static Web App ( similar discussion).
You can do so from here: https://github.com/settings/connections/applications/c98ca422fdc82b48e87d
Just in case if you are not able to reach here using the link above, please follow the steps below,
• Go to GitHub Settings from top right corner
• Select Applications from the left side menu
• Go to Authorized OAuth Apps from the tabs shown
• And then select Azure Static Web Apps from the list
If the answer helped (pointed, you in the right direction) > please click Accept Answer - it will benefit community members and be much appreciated.